Override trait's generic method without casting

I was planning to have a trait with "value" attribute that can be extended by multiple classes. I need to then be able to compare different instances of that trait between each other. Firstly I want to check the value defined on the trait - if thats the same across two instances, then I want to trigger child-specific method that will compare two child instances of the same type with each other.

I hope I explained that clearly enough...

I have below code written, but the ChildOne class doesnt compile - the error I am getting:

class ChildOne needs to be abstract, since method childCheck in trait
ParentType of type (other: ChildOne.this.T)Boolean is not defined
(Note that ParentType.this.T does not match com.cards.ChildOne)